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THE NEWARK PUBLIC SCHOOLS
THE OFFICE OF MATHEMATICS
THE NEWARK PUBLIC SCHOOLS
MATHEMATICS
THE OFFICE OF
Grade 6
The Number System
6.NS.5 and Review
Answer Pages
2012 COMMON CORE STATE STANDARDS ALIGNED MODULES
Lesson 1-Introductory Tasks (pg. 4)
93° warmer
Guided Practice (pg. 5)
1. – 6.1, - 3, - .8, - , .5, , 1.2, 5
2. answers will vary
3. a. – 6
b. + 6
c. – 5
-12, - 7, - 6, - 5, 0, + 6
d. – 7
e. – 12
f. 0
Collaborative Work (pg. 6)
1. a + b = 0, Same distance from “0” means positive and negative. Sum is “0”.
2. Negative numbers: a – 2 , a + b, ab + 1
Journal Question
D It is the only point indicated between – 10 and – 20.
Homework (pg. 7)
1. + 14
2. – 8
3. 0
4. - 3
5. -2.55
Lesson 2-Introductory Task (pg. 8)
Winning score: 47
Worst score: 69
Guided Practice (pg. 9)
1.
a. + 35
b. – 1
c. + 75
d. + 8
e. + 0.25
f. – 5
g. – 36
h. – 8
i. – 25
j. – 23
2. - 21° F
3. 550 feet below sea level
4. 150 feet below sea level
5. 59 yards
6. change: - 26° C
average: - 13°C
Team’s overall score: 61
Collaborative Work (pg. 10)
1. 20°
2. 572 feet below sea level
3. $57.00
4. 1. Below sea level
2. 5562 feet
3. Zero feet above sea level
5. – 10 meters
6. increase: 90°C
after 1 minute: 18 ° C
7. 186°F
8. 75°C warmer
Journal Question
+ 7 yard gain on the 4th down
(explanations will vary)
Homework (pg. 11)
1. - 25°F
2. – 2, - , 0, .05, , .55, 1.1
3. Numbers decrease as you move to the left on the number line – they increase as you move to the
right.
4. 5 + (4 – 3) x 2
5. 28 minutes (-5), 30 minutes (-3), 37 minutes (+ 4), 40 minutes
6. +30
7. 4° per 10,000 feet
8. - 7° C
9. $76.9 M
Lesson 3-Golden Problem (pg. 12)
(see rubric pg. 13)
Review (pg. 15)
1. 3 people share
pound of chocolate. How much of a pound of chocolate does each person get?
2. Manny has yard of fabric to make book covers. Each book is made from yard of fabric. How many
book covers can Manny make?
3. Michelle has ¾ cup of pancake mix. Each pancake uses 1/8 cup of pancake mix. How many pancakes
can Manny make?
4.
A rectangular strip of land has an area of 5/6 square yards. The strip is 2/3 yards long. How wide, in
yards, is the strip of land?
5.
Look at the number sentence below: 7 
6
6.
5 1


6 12
=7
7. How many ¾ cup servings are in 4 ½ cups of chocolate ice cream? Show or explain how you found
your answer.
8. Look at the number sentence below:
2 1
 
3 6
a) Write a story problem that can be solved using this number sentence.
b) Solve your story problem.
c) Use the model below to show or explain your answer.
Answer: Story problems may vary but should provide a context for finding the number of sixths in
two-thirds with an answer 4. The model shows that
2 1
  4 (there are 4 shaded sections).
3 6
Review (pg. 16)
9. Which picture models
1 1
 ?
2 8
A.
B.
C.
D.*
10.…The player’s score equals par.
11.…The elevation of Mount Washington in New Hampshire is 6,288 feet. This means that Mount
Washington is 6,288 feet above sea level. The elevation of Death Valley is -282 feet. What does an
elevation of -282 feet mean?
Answer: An elevation of -282 feet means 282 feet below sea level.
12.…………..Mark an X on the number line that shows the location of the opposite of Point A.
Answer:
(pg. 17)
13.…………Shade the thermometer to show -8°F.

Answer: Thermometer is shaded up to -8°F.
14.,Look at the coordinate plane below.
a) What are the coordinates of Point A?
b) Graph the point (3, -5) and label it Point B.
Answer: The coordinates of Point A is (-4, 6) and the correct location of the point (3, -5) is graphed
on the coordinate plane.
Partial Credit: The student answers only one question correctly.
No Credit: The student answers neither question correctly.
(pg. 18)
15. Which number on the number line is the same distance from both Point A and Point B?
Show or explain how you found your answer.
Answer: 0 with an explanation that may include:



Identifying the graphed points as opposites.
Identifying the distances from zero and/or absolute value
Counting in from both ends
Partial Credit: Correct answer, 0, with an incorrect or missing explanation, OR an incorrect answer
with an explanation that demonstrates understanding of absolute value or distance from zero of
integers and their opposites.
No Credit: Incorrect answer with an incorrect or missing explanation.
16. If 6 is 30% of a value, what is that value? (Solution: 20)
17. On a coordinate plane, a line segment is drawn between Point A (-3, 4) and Point B (3, 4). What are
the coordinates of the point on the line segment that is half way between Points A and B?
Show or explain how you found your answer. You may use the coordinate plane below to help
you find the answer.
Answer: (0, 4) with an explanation that may include:


The coordinate plane with points graphed correctly
Absolute value/distance from (0,4)
Partial Credit: Correct answer, 0, with an incorrect or missing explanation, OR an incorrect answer
with an explanation that demonstrates understanding of absolute value or distance from zero of
integers and their opposites.
No Credit: Incorrect answer with an incorrect or missing explanation.
(pg. 19)
18. If the point (3,-5) is reflected across the x-axis, what are the coordinates of the new point?
Show or explain how you found your answer. You may use the coordinate plane below to help you
find the answer.
Answer: (3, 5) with an explanation that may include:


The coordinate plane with points graphed correctly
Absolute value/distance from (3,0)
Partial Credit: Correct answer, (3, 5), with an incorrect or missing explanation, OR an incorrect answer
with an explanation that demonstrates understanding of use of coordinates and absolute value to find
distances between points with the same first coordinate or the same second coordinate.
No Credit: Incorrect answer with an incorrect or missing explanation.
19.
Use the information below to answer the questions.
State
Record Low temperature (°F)
Connecticut
-32
Maine
- 48
Massachusetts
-35
New Hampshire
-47
Rhode Island
-25
Vermont
-50
Which state had the coldest temperature? Show or explain how you found your answer.
Answer: Vermont with an explanation that may include:
 Number line(s) showing the location of each temperature
 Understanding that colder temperatures are further away from zero on a number line
 The absolute value of -50 is greater than the absolute values of the other numbers, which
means it is further away from 0°F than the others.
Partial Credit: Correct answer, Vermont, with an incorrect or missing explanation, OR an incorrect
answer with an explanation that demonstrates understanding that for negative degrees Fahrenheit,
the greater the absolute value or distance from 0°F, the colder the temperature.
No Credit: Incorrect answer with an incorrect or missing explanation.
20.….A whale is swimming at a depth of -25 feet. A submarine is located at a depth of -40 feet. Sea
level is 0 feet. Which is deeper, the whale or the submarine?
Show or explain how you know your answer is correct.
Answer: The submarine with an explanation that may include:
 Number line(s) showing the location of the whale and the submarine
 The absolute value of -40 is greater than the absolute value of -25, which means -40 is
further away from the surface (0).
Partial Credit: Correct answer, submarine, with an incorrect or missing explanation, OR an incorrect
answer with an explanation that demonstrates understanding that for negative depth, the greater
the absolute value or distance from the surface, the deeper the object is located from the surface.
No Credit: Incorrect answer with an incorrect or missing explanation.